Two points are chosen at
random in the interval [0, 1]; X denotes the first point chosen and Y denotes
the second point chosen. Random variable U gives the type of triangle that can
be formed from the three sub-intervals:

- U = 0: the pieces do not form a triangle.
- U = 1: the pieces form an obtuse triangle.
- U = 2: the pieces form an acute triangle.

- U = 2 consists of the 2 interior regions.
- U = 1 consists of the 6 middle regions.
- U = 0 consists of the outer regions.

## Software/Applets used on this page

an applet from PSOL from UAH

## Glossary

### acute

An angle less than 90 degrees.

### cut

A set of edges whose removal separates a network into two parts, where one part contains the source and the other part contains the sink.

### density

the ratio of the mass of an object to its volume

### function

A rule that connects one value in one set with one and only one value in another set.

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### obtuse

an angle between 90 and 180 degres

### random variable

a variable that represents the values obtained when measurements are taken from a population in the real world; it must take a numerical value.

### sample space

The list of all possible outcomes from an experiment.

### variable

A value which is unknown and free to vary, often denoted by x or y.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

AQA AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

AQA AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

CBSE XII (India) | Probability | Probability | Repeated independent (Bernoulli) trials and binomial distribution | - |

CBSE XI (India) | Statistics and Probability | Probability | Random experiments, outcomes, sample spaces (set representation) | - |

CCEA A-Level (NI) | S1 | Probability | Experimental | - |

CIE A-Level (UK) | S1 | Probability | Experimental | - |

Edexcel A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

Edexcel AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

Edexcel AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

I.B. Higher Level | 5 | Probability | Experimental | - |

I.B. Standard Level | 5 | Probability | Experimental | - |

Methods (UK) | M15 | Probability | Experimental | - |

I.B. (MSSL) | 3 | Probability | Experimental | - |

OCR A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

OCR AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

OCR MEI AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

OCR-MEI A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

Pre-Calculus (US) | E4 | Probability | Experimental | - |

Pre-U A-Level (UK) | Prob | Probability | Experimental | - |

Scottish (Highers + Advanced) | HS | Probability | Experimental | - |

Scottish Highers | S | Probability | Experimental | - |

Universal (all site questions) | P | Probability | Experimental | - |

WJEC A-Level (Wales) | S1 | Probability | Experimental | - |